Space of modular forms of level 304, weight 2, and Character 304.i

• Label: 304.2.i
• Level: $304$
• Weight: $2$
• Character orbit: 304.i
• Rep. character: $\chi_{304}(49,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $18$
• Newform subspaces: $6$
• Sturm bound: $80$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(80\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(304, [\chi])\).

	Total	New	Old
Modular forms	92	22	70
Cusp forms	68	18	50
Eisenstein series	24	4	20

Trace form

\( 18 q + 3 q^{3} - q^{5} + 8 q^{7} - 6 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(304, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
304.2.i.a	$304$	$2$	304.i	19.c	$3$	$2$	$1$	$2.427$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
304.2.i.b	$304$	$2$	304.i	19.c	$3$	$2$	$1$	$2.427$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
304.2.i.c	$304$	$2$	304.i	19.c	$3$	$2$	$1$	$2.427$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+4q^{7}+2\zeta_{6}q^{9}-3q^{11}+\cdots\)
304.2.i.d	$304$	$2$	304.i	19.c	$3$	$2$	$1$	$2.427$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+(4-4\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
304.2.i.e	$304$	$2$	304.i	19.c	$3$	$4$	$2$	$2.427$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
304.2.i.f	$304$	$2$	304.i	19.c	$3$	$6$	$3$	$2.427$	6.0.2696112.1	None		$2$	$0$	\(0\)	\(1\)	\(-1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(304, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(304, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 2}\)